Details

analyze1.2s (18.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample81.0ms (1.3%)

Algorithm

1×

intervals

Results

48.0ms	129×	body	2048	valid
15.0ms	60×	body	1024	valid
7.0ms	40×	body	512	valid
1.0ms	12×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
1.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series9.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
2.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
628×	`fma-def_binary64`
405×	`fma-neg_binary64`
337×	`associate-/l*_binary64`
292×	`associate-/r*_binary64`

Counts

63 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1379
1	209	1264
2	549	1261
3	1434	1259
4	4502	1259
5	5039	1259

prune50.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Error

0.7b

Counts

94 → 5

Alt Table

Status	Error	Program
	1.7b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
▶	0.7b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

Compiler

Compiled 1371 to 992 computations (27.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
0.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

series1.3s (21.3%)

Counts

2 → 24

Calls

2 calls:

714.0ms	(log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
635.0ms	(expm1.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

simplify108.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
308×	`times-frac_binary64`
295×	`sub-neg_binary64`
284×	`neg-sub0_binary64`
245×	`unsub-neg_binary64`

Counts

46 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	947
1	43	873
2	84	873
3	244	873
4	908	873
5	2307	873
6	4180	873
7	4814	873
8	4842	873

prune67.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	176	3	179

Error

0.7b

Counts

179 → 3

Alt Table

Status	Error	Program
	2.2b	(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))
▶	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	3.4b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 2052 to 1529 computations (25.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series1.0ms (0%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1816×	`fma-def_binary64`
578×	`sqr-pow_binary64`
513×	`associate-l_binary64`
493×	`*-commutative_binary64`
354×	`unswap-sqr_binary64`

Counts

10 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	211
1	29	182
2	45	182
3	77	182
4	161	182
5	401	182
6	1153	182
7	2143	182
8	2224	182
9	2406	182
10	2629	182
11	2908	182
12	3210	182
13	4308	182
14	4749	182
15	4748	182

prune23.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	9	2	11
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	10	4	14

Error

0.7b

Counts

14 → 4

Alt Table

Status	Error	Program
	1.7b	(*.f64 (sqrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (sqrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
▶	0.7b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	3.4b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	2.2b	(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))

Compiler

Compiled 397 to 299 computations (24.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
✓	0.8b	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

2 → 82

Calls

2 calls:

7.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
0.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series8.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

6.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
1.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify152.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`
328×	`unsub-neg_binary64`
317×	`fma-neg_binary64`
288×	`distribute-lft-in_binary64`

Counts

94 → 153

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	3370
1	215	2716
2	598	2070
3	1781	2070
4	4258	2055
5	4987	2055
6	4859	2055

prune158.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	152	5	157

Error

0.7b

Counts

157 → 5

Alt Table

Status	Error	Program
✓	0.7b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	2.7b	(fma.f64 (/.f64 (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 PI.f64) (cbrt.f64 2)) (neg.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	2.2b	(expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)))
	62.9b	(/.f64 (-.f64 (.f64 (/.f64 PI.f64 4) PI.f64) (pow.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 6)) (+.f64 (.f64 1/2 PI.f64) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	3.4b	(expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (log1p.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))

Compiler

Compiled 4864 to 3618 computations (25.6% saved)

regimes147.0ms (2.3%)

Accuracy

Total 0.0b remaining (2.1%)

Threshold costs 0.0b (2.1%)

Compiler

Compiled 4066 to 3092 computations (24% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	22	21
2	29	21
3	36	21
4	41	21
5	44	21
6	45	21
7	42	21

end0.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample2.7s (41.8%)

Algorithm

1×

intervals

Results

1.5s	3983×	body	2048	valid
526.0ms	2047×	body	1024	valid
179.0ms	962×	body	512	valid
58.0ms	470×	body	256	valid
37.0ms	535×	body	128	valid
2.0ms	3×	body	4096	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 175 to 131 computations (25.1% saved)

Details

analyze1.2s (18.7%)

sample81.0ms (1.3%)

simplify76.0ms (1.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite5.0ms (0.1%)

series9.0ms (0.1%)

simplify81.0ms (1.3%)

prune50.0ms (0.8%)

localize10.0ms (0.2%)

rewrite2.0ms (0%)

series1.3s (21.3%)

simplify108.0ms (1.7%)

prune67.0ms (1.1%)

localize6.0ms (0.1%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify128.0ms (2%)

prune23.0ms (0.4%)

localize8.0ms (0.1%)

rewrite17.0ms (0.3%)

series8.0ms (0.1%)

simplify152.0ms (2.4%)

prune158.0ms (2.5%)

regimes147.0ms (2.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.7s (41.8%)

Profiling